Moderators locked up the previous thread before I had the chance of replying to the monodimensional replies that turned the previous thread
into US party politics/climate denial (there are probably other fora for that) frenzy.
Anyway, it's really simple in general: (crude) oil production has a carbon footprint, not just used lubricant disposal where everyone jumped into right away. So when you change your engine oil at the rate of 3 times of normal then you are being three times as wasteful environmentally. This does not have anything to do with how the oil is recycled (which you have no control over), be it burned in a energy plant where it is happening anyway until the plant is decommissioned (regardless the origin of the fuel) or re-refined into usable lubricant which is many times environmentally friendly but it does not remove the earlier steps of production from the overall footprint.